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- Title
Testing collinearity of vector time series.
- Authors
McElroy, Tucker S; Jach, Agnieszka
- Abstract
We investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.
- Subjects
TIME series analysis; STATISTICAL hypothesis testing; SCHUR complement; SPECTRAL energy distribution; DENSITY matrices
- Publication
Econometrics Journal, 2019, Vol 22, Issue 2, p97
- ISSN
1368-4221
- Publication type
Article
- DOI
10.1093/ectj/uty002